Avast's Safe Zone browser is based upon Chromium, which is what several major browsers (including Chrome and Opera) are also founded upon.
It theoretically offers a 'safer browsing experience' but I can see no advantage in using it myself.
Further, the company behind Avast has been known to make mistakes in developing Safe Zone, actually putting web users at greater risk of threats than when using other browsers:
http://www.pcworld.com/article/3030319/security/researcher-finds-serious-flaw-in-chromium-based-avast-safezone-browser.html
I'll continue to decline those offers to install it; I suggest that you should do so too.